set theory/ graph theoryparallel edgesspanning setfactorizationedge setedge coloringsOne edge of a graph G is taken as a basic unit, regarded as the set of its two nodes. Two edges are called parallel (or indep
By using this technology, non-solutions can be simultaneously deleted from multiple edges in the graph, significantly reducing the number of biological operations and substantially improving the computing efficiency. These parallel concepts render it feasible to solve larger-scale complex problems. The ...
In a bipartite graph G=(V1∪V2,E), the vertex sets V1 and V2 are disjoint and for all edges in E, one of the endpoints belongs to V1 and the other belongs to V2. For a vertex v∈V1∪V2, the neighborhood of v is defined as Γ(v)={u:{u,v}∈E}. Clearly if v∈V1 th...
Unavoidable vertex-minors in large prime graphs O-joung KwonSang-il Oum Oct 2014 A graph is prime (with respect to the split decomposition) if its vertex set does not admit a partition (A,B) (called a split) with |A|, |B| >= 2 such that the set of edges joining A and B induce...
the graph dataset Wikipedia has a large number of edges of 101,355,853. Hash-table-based method requires more waiting time to synchronize and update information. However, the latency in the information synchronization is reduced in our method, which enlarges the speedup of our method dramatically...
TheGNNFandGNNPmodels differ in the architecture of the attention head as seen in Fig.1, a schematic of the prediction logic implemented in our models. InGNNF, the protein and ligand adjacency matrices are combined into a single matrix, and edges are added between protein and ligand nodes base...
The input of libgrape-lite is formatted following theLDBC Graph Analyticsbenchmark, with two files for each graph, a.vfile for vertices with 1 or 2 columns, which are a vertex_id and optionally followed by the data assigned to the vertex; and a.efile for edges with 2 or 3 columns, ...
– A node p at level k > 0 has nk outgoing edges, labelled from 0 to nk−1. The edge labelled by ik points to a node q at level k−1; we write p[ik] = q. – Given nodes p and q at level k, if p[ik] = q[ik] for all ik ∈ Sk, then p = q, i.e., there...
We provide a parallel algorithm that finds an induced subgraph of a given graph G that contains approximately half the edges of G. This is used for the parallel construction of a nearly optimal group testing strategy in the case of two defective elements....
The number of links or edges in a hypercube are n 2n–1. On the 'C40-based n=6 hypercube, 192 cables will be required. Port connections are assigned via an iterative algorithm. 33 Six Properties of the Hypercube Six properties [8, 11, 14] are unique to the hypercube and can be ...